In a composite body made of two non-metal or two metal elements or one non-metal element and one metal element (German patent document no. 197 04 357), the bonding material is made of metal, e.g., Al, Cu, Zn, Mg, Ag, Au, Si, Fe, Ti, Ge, Sn, or the like, or an alloy made of these metals. The bonding material is introduced through a casting process, e.g., diecasting or infiltration. For this purpose, the two elements are placed tightly and directly against one another or on top of one another and are encapsulated. The liquefied bonding material is able to migrate between the two elements because of the fine surface roughness which they always have and therefore permanently bond the two elements to one another. In order to increase the quantity of bonding material penetrating between the two elements, one or even both of the surfaces of the adjoining elements facing toward one another is roughened. This roughening may be performed through simple grinding or by implementing groove-shaped channels.